Suppose that a function $\displaystyle f$ is analytic throughout the finite plane except for a finite number of singular points $\displaystyle z_1, z_2, \ldots, z_n$. Show that

$\displaystyle \text{Res}_{z=z_1}f(z)+\text{Res}_{z=z_2}f(z)+ \cdots + \text{Res}_{z=z_n}f(z)+\text{Res}_{z=\infty}f(z)=0$.

I don't see how to show this right now. Any hints on where to go would be nice. Thank you.